Control of the spread of TB-HIV/AIDS coinfection using optimal control

The condition in which an individual is affected by TB and HIV/AIDS in his body is called a TB-HIV/AIDS coinfection. This research aims to minimize the populations of TB-HIV/AIDS coinfection with a minimum expenditure on medical expenses, that means minimizing the objective’s function ( ) or purpose function. In this research, modification of the model was carried out by adding the treatment population for HIV patients with ARV ( ). The population used was 11 classes with the use of three controls including treatment for individuals with latent TB ( ), active TB ( ), and HIV ( ). After performing numerical simulation using the forward backward fourth order Runge-Kutta, the results show that scenario 7 is the best scenario in controlling the spread of TB-HIV/AIDS coinfection because it resulted a minimum value of 1401,44. This means that providing the treatment for individuals with latent TB, active TB, and HIV in tandem can reduce the populations of TB-HIV/AIDS coinfection in the minimum treatment cost.